1. Field of the Invention
The present invention relates to a method of generating halftone threshold data to convert continuous tone image data into binary image data or multi-valued image data for a color halftone image output apparatus in printing applications, such as a color printer, an image setter, a CTP (Computer To Plate) apparatus, a CTC (Computer To Cylinder) apparatus, a DDCP (Direct Digital Color Proof) apparatus, or the like.
2. Description of the Related Art
Halftone image output apparatus record a halftone image on a recording medium such as a printing sheet, a film, or the like by comparing continuous tone image data obtained from an original image with halftone threshold data to generate binary or multi-valued halftone image data, and controlling a laser beam or the like based on the generated binary or multi-valued halftone image data.
FIG. 9 of the accompanying drawings shows the corresponding relationship between a single dot cell 2 made of a plurality of halftone threshold data and pixels 4 formed by a laser beam or the like on a recording medium in a main scanning direction which is indicated by the arrow X and an auxiliary scanning direction which is indicated by the arrow Y. The halftone threshold data are established with respect to the respective pixels 4 in the dot cell 2.
When a plurality of halftone images are superposed to generate a halftone image, a moirxc3xa9 pattern in the halftone image is reduced if each dot cell 2 is established obliquely at a certain angle xcex8 (screen angle xcex8) to the main scanning direction X or the auxiliary scanning direction Y. The number of tones or gradations of the halftone image is normally determined by the number of pixels 4 which make up each dot cell 2. The output resolution (dpi) of a halftone image output apparatus is defined as the number of pixels 4 per inch, and the screen ruling (halftone screen period) (lpi) is defined as the number of dot cells 2 per inch.
FIG. 10 of the accompanying drawings shows, by way of example, a halftone image generated using the halftone threshold data of the dot cell 2 shown in FIG. 9. The halftone image output apparatus compares the magnitude of continuous tone image data with the magnitude of the halftone threshold data established with respect to the respective pixels 4 in the dot cell 2, thus generating binary image data. Halftone dots 6, shown hatched, represent image areas where the pixels 4 are blackened by a laser beam, for example, based on the generated binary image data.
In order to generate a color halftone image using a halftone image output apparatus, it is necessary to generate halftone images in different colors C, M, Y, K, for example, and superpose the generated halftone images in those colors. When the halftone images are superposed, the generation of a moirxc3xa9 pattern due to the halftone screen period of the dot cells 2 in the halftone image in each color should be avoided. The halftone screen period of the dot cells 2 occurs in a direction along corners a1, a2 of each dot cell 2 and a direction, perpendicular thereto, along corners a1, a4 of each dot cell 2. The pitch of the moirxc3xa9 pattern is smaller as the angles between the directions of the halftone screen period of the dot cells 2 in the superposed halftone images in the different colors differ more widely from each other. The screen angles xcex8 of the colors are established such that the difference between the screen angles xcex8 of the colors C, M, K, which are loud colors, is a maximum, i.e., 30xc2x0. Traditionally, the screen angles xcex8 of the colors C, M, K are set to 15xc2x0, 45xc2x0, and 75xc2x0, respectively, and the screen angle xcex8 of the color Y is set to 0xc2x0. Since the color Y is a visually less intensive color, the difference between its screen angle and the screen angles of the other colors is set to 15xc2x0.
FIG. 11 of the accompanying drawings shows vectors representing the halftone screen periods of the colors and the period of a moirxc3xa9 pattern generated thereby. The magnitudes of the vectors are proportional to the screen ruling (halftone screen period). A vector D1 representing a color image having a screen angle xcex81 and a halftone screen period d1 and a vector D2 representing a color image having a screen angle xcex82 and a halftone screen period d2 make up a vector D12 representing the direction and period of a primary moirxc3xa9 pattern generated by direct interference between the two halftone screen periods. The vector D12 of the primary moirxc3xa9 pattern has components represented by (d2xc2x7cos xcex82xe2x88x92d1 cos xcex81, d2xc2x7sin xcex82xe2x88x92d1xc2x7sin xcex8l).
As described above, a color halftone image is formed by three or more superposed images in different colors. If the color images are represented by respective vectors D1, D2, D3 having respective screen angles xcex81, xcex82, xcex83 (xcex81 less than xcex83 less than xcex82, see FIG. 11) and respective halftone screen periods d1, d2, d3, then since general color images are periodic at equal pitches in two perpendicular directions, the vectors D1, D2, D3 are associated with respective vectors D1xe2x8axa5, D2xe2x8axa5, D3xe2x8axa5 which are perpendicular to the vectors D1, D2, D3 and have halftone screen periods equal to those of the vectors D1, D2, D3. When the three color images are superposed according to the relationship shown in FIG. 11, then because the vector D12 representing a primary moirxc3xa9 pattern due to the interference between the vectors D1, D2 and the vector D3xe2x8axa5 have similar magnitudes and angles, a secondary moirxc3xa9 pattern that can easily be recognized by human vision is generated if the two vectors D12, D3xe2x8axa5 deviate slightly from each other.
In order to eliminate such a secondary moirxc3xa9 pattern, the vector D12 may be equalized to the vector D3xe2x8axa5. Specifically, if the following conditions are satisfied:
d3xc2x7cos xcex83=d1xc2x7cos xcex81xe2x88x92d2xc2x7cos xcex82xe2x80x83xe2x80x83(1) 
xe2x80x83d3xc2x7sin xcex83=d2xc2x7sin xcex82xe2x88x92d1xc2x7sin xcex81xe2x80x83xe2x80x83(2)
then the period of the secondary moirxc3xa9 pattern becomes infinitely large, making the secondary moirxc3xa9 pattern invisible to human vision. More specifically, when the screen angle xcex8 of the color image of M is set to 45xc2x0, the period of the primary moirxc3xa9 pattern generated by the color images of C, K whose screen angles xcex8 are set to 15xc2x0 and 75xc2x0, respectively, and the halftone screen period of the color image of M whose screen angle xcex8 is set to 45xc2x0 are equalized to each other, avoiding the generation of a secondary moirxc3xa9 pattern (see Japanese Patent Publication No. 2578947 for details).
In order to satisfy the conditions according to the above equations (1), (2), it is necessary to set the screen angles xcex81 through xcex83 and the halftone screen periods d1 through d3 of the respective colors to appropriate values.
According to a process of digitally generating the halftone threshold data that make up the dot cell 2 shown in FIG. 9, the halftone threshold data are generated according to the condition of a rational tangent. The condition of a rational tangent is a condition in which when a corner al of the square dot cell 2 is placed on a grid of pixels 4, other corners a2 through a4 of the dot cell 2 are also placed on the grid of pixels 4. With respect to the dot cell 2 having the screen angle xcex8, there are established integers m, n which are mutually prime, as represented by the following equation (3):
xcex8=tanxe2x88x921 (n/m)xe2x80x83xe2x80x83(3) 
If the dot cell 2 has a pitch P, which represents the distance between the corners a1, a2 with pixels 4 serving as a unit, then the coordinates of the corners a1 through a4 in the main scanning direction X and the auxiliary scanning direction Y are established as shown in FIG. 9 using the corner al as the origin.
In order for the dot cell 2 having the screen angle xcex8 and the pitch P to satisfy the condition of a rational tangent, the coordinates of the corners a1 through a4 should be expressed by integral values. If A, B represent integers, then it is a necessary and sufficient condition to satisfy the following equations:
Pxc2x7cos xcex8=Axe2x80x83xe2x80x83(4) 
Pxc2x7sin xcex8=Bxe2x80x83xe2x80x83(5) 
From the equations (4), (5), the following equation (6) is obtained:
tan xcex8=B/Axe2x80x83xe2x80x83(6) 
If k1 is an integer other than 0, then the following relationships are obtained from the equation (6):
A=k1xc2x7mxe2x80x83xe2x80x83(7) 
B=k1xc2x7nxe2x80x83xe2x80x83(8) 
Putting the equation (7) into the equation (4), the following equation (9) is obtained:                                                                         P                =                                                      A                    /                    cos                                    ⁢                                      xe2x80x83                                    ⁢                  θ                                                                                                        =                                  k1                  ·                                      √                                          (                                                                        m                          2                                                +                                                  n                          2                                                                    )                                                                                                          "AutoLeftMatch"                            (        9        )            
The equation (9) generally represents the condition in which the dot cell 2 having the screen angle xcex8 and the pitch P satisfies a rational tangent, with parameters m, n representing the screen angle xcex8 of the dot cell 2 expressed by the equation (3) and the pitch P of the dot cell 2. The screen ruling (halftone screen period) is indicated by the reciprocal of Pxc2x7q where q represents the size of each pixel 4. Therefore, with respect to the color images whose screen angles xcex8 are 0xc2x0 and 45xc2x0, dot cells 2 capable of establishing an accurate screen angle xcex8 can be determined with respect to a number of screen rulings according to the relationship of the equations (3), (9).
However, with respect to the color images whose screen angles xcex8 are 15xc2x0 and 75xc2x0, dot cells 2 having screen angles close to 15xc2x0 and 75xc2x0 can only be determined with respect to a limited number of screen rulings. Therefore, the degree of freedom of dot cells 2 that can be selected is low.
According to another process shown in FIG. 12 of the accompanying drawings, a supercell 9 is made up of dot cells 8, and a screen angle xcex8 and a screen ruling are established to satisfy the condition of a rational tangent in which the supercell 9 has corners B1 through B4 placed on the grid of pixels 4. For details of the generation of a halftone image in relation to the supercell 9, reference should be made to, for example, a book entitled xe2x80x9cPostscript screeningxe2x80x9d written by Peter Fink, published by MDN corporation on Aug. 11, 1994, 1st edition, 1st printing.
The condition of a rational tangent shown in FIG. 12 will be considered below. First, parameters m, n capable of expressing the screen angle xcex8 of the supercell 9 according to the equation (3) are established. It is assumed that the number of dot cells 8 making up the supercell 9 is represented by xcex12 and k2 represents an integer other than 0. The coordinates of the corner B2 are set to (k2xc2x7m, k2xc2x7n). In FIG. 12, since cos xcex8 is expressed using the parameters m, n and using the pitch P as follows:
cos xcex8=m/(m2+n2)=k2xc2x7m/(Pxc2x7xcex1)xe2x80x83xe2x80x83(10) 
the relationship between the pitch P of the dot cells 8 and the parameters m, n, xcex1 at the time the supercell 9 whose screen angle xcex8 is expressed by the equation (3) satisfies the condition of a rational tangent is represented by:
P=k2/xcex1xc2x7(m2+n2)xe2x80x83xe2x80x83(11) 
By constructing the supercell 9 of a number of dot cells 8 which satisfy the equation (11), it is possible to make the screen angle xcex8 as close to 15xc2x0 and 75xc2x0 as possible, and the degree of freedom for selecting screen rulings is increased.
When the supercell 9 and dot cells 2 individually satisfying the condition of a rational tangent are combined with each other, color images are generated using the supercell 9 at 15xc2x0 and 75xc2x0, and color mages are generated using dot cells 2 according to a rational tangent at 0xc2x0 and 45xc2x0, the screen angles xcex8 and the pitch P are established highly accurately, and a halftone image with the possibility of a moirxc3xa9 pattern being highly reduced can be generated.
Recently, it has become possible to establish output conditions of a low output resolution and many screen rulings, using the supercell 9, to output a highly defined halftone image of high gradations. Since the output resolution is low, the number of gradations which can be expressed by one dot cell 8 is small. However, an image of many gradations can be expressed by clustering a plurality of dot cells 8 and optimizing the layout of halftone threshold data thereof. According to this process, an image which has heretofore been outputted at an output resolution of 2400 dpi (dots per inch) and a screen ruling of 175 lpi (lines per inch) can be outputted at an output resolution of 1200 dpi and a screen ruling of 175 lpi with an equivalent or higher image quality. As a result, a halftone image can be outputted at a high speed.
If a halftone image output apparatus having output conditions of a low output resolution and many screen rulings uses dot cells 2 satisfying the condition of a rational tangent for color images whose screen angles xcex8 are 0xc2x0 and 45xc2x0, then since the shapes of halftone dots 6 shown in FIG. 10 are identical with respect to the same halftone area percentage, the halftone dots 6 are simultaneously held in contact with each other in the vicinity of a halftone area percentage of 50%, in particular, in the range of gradations where the halftone area percentage is gradually higher. Consequently, the halftone image tends to suffer a tone jump. This tendency is greater as the output resolution is lower.
It is a general object of the present invention to provide a method of generating halftone threshold data to avoid the occurrence of a tone jump and make a moirxc3xa9 pattern less visible in a halftone image output apparatus having output conditions of a low output resolution and many screen rulings.
Another object of the present invention to provide a method of generating halftone threshold data to keep a sufficient number of gradations in a halftone image output apparatus having output conditions of a low output resolution and many screen rulings.
Still another object of the present invention to provide a method of generating halftone threshold data to reduce a moirxc3xa9 pattern produced due to an interference between superposed color images in a halftone image output apparatus having output conditions of a low output resolution and many screen rulings.
Yet still another object of the present invention to provide a method of generating halftone threshold data to make the screen angle of each color image close to a desired angle and also to make the screen ruling close to a desired screen ruling in a halftone image output apparatus having output conditions of a low output resolution and many screen rulings.
According to the present invention, there is provided a method of generating halftone threshold data for color images of C, M, Y, K to reproduce a color image, comprising the steps of setting dot cells made up of the halftone threshold data under output conditions including an output resolution of 2000 dpi or less and an output resolution/halftone screen period ratio to 8 dpi/lpi or less, setting the dot cells of at least the three color images of C, M, K under the condition of a non-rational tangent, and setting halftone screen periods and screen angles of the three color images of C, M, K such that a period and an angle of a primary moirxc3xa9 pattern produced when two of the three color images of C, M, K are superposed are substantially equal to a halftone screen period and a screen angle of the remaining one of the three color images of C, M, K.
Since the layout of the halftone threshold data differs from dot cell to dot cell, a tone jump is not visually recognized when halftone images having the same halftone area percentage are formed. This advantage is obtained especially for dot cells that are set under output conditions including an output resolution of 2000 dpi or less and an output resolution/halftone screen period ratio to 8 dpi/lpi or less.
The above and other objects, features, and advantages of the present invention will become more apparent from the following description when taken in conjunction with the accompanying drawings in which preferred embodiments of the present invention is shown by way of illustrative example.